Least Common Multiple (LCM) of 192 and 73
The least common multiple (LCM) of 192 and 73 is 14016.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 192 and 73?
First, calculate the GCD of 192 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 73 = 2 remainder 46 |
| 2 | 73 ÷ 46 = 1 remainder 27 |
| 3 | 46 ÷ 27 = 1 remainder 19 |
| 4 | 27 ÷ 19 = 1 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 21 | 3633 |
| 73 and 188 | 13724 |
| 132 and 149 | 19668 |
| 72 and 178 | 6408 |
| 29 and 12 | 348 |